Question

The value of a car depreciated by 10% in the first 2 years and by 8% in the third year. Express the total depreciation of the car as a single per cent during the three years.

Answer 1

Let value of car be Rs x. 

${\displaystyle {\text{V}}_0}$ =Rs x ; n = 3 ; r = 10%  for first 2 years and 8% for 3rd year .

${\displaystyle \therefore {\text{V}}_{\text{t}}={\text{V}}_0\times {(1-\frac{\text{r}}{100})}^{\text{n}}}$

${\displaystyle \Rightarrow {\text{V}}_{\text{t}}=\text{Rs} \text{x} \times {(1-\frac{10}{100})}^2(1-\frac{8}{100})}$

${\displaystyle \Rightarrow {\text{V}}_{\text{t}}=\text{Rs} \text{x} \times \frac{9}{10}\times \frac{9}{10}\times \frac{23}{25}}$

${\displaystyle \Rightarrow {\text{V}}_{\text{t}}=\text{Rs} \text{x} \times \frac{1863}{2500}}$

${\displaystyle \Rightarrow {\text{V}}_{\text{t}}=\text{Rs} 0.7452 \text{x}}$

Depreciation in the value of car

= Rs (x - 0.7452 x) = Rs 0.2548 x  

Percentage change in depreciation 

${\displaystyle =\frac{0.2548 \text{x}}{\text{x}}\times 100}$

= 25.48 %

Percentage change = 25.48 %